Functional enrichment analysis

library(topGO)
library(knitr)   # to use kable()
library(limma)   # to use vennDiagram()
library(ggplot2)
TAG <- params$TAG
VAR <- params$VAR
ANNOTATION <- list(genes = '../2019-07-26/genes/annotation.txt',
                   isoforms = '../2019-07-26/transcripts/annotation.txt')
TAGDIR <- paste0('../2020-01-08/', TAG, '/')

Introduction

This is the enrichment analysis for genes regulated by hatching. Because I quantified the association of expression with hatching in two different ways, this document has two sections. Section Variance reports the enrichment analysis performed with genes ordered by the proportion of expression variance explained by hatching. Note that some genes with low variance may still be highly associated with hatching, even if the fold change between levels of this factor is low. Section Differential expression uses an ordering of genes based on the significance of the differential expression between levels of hatching, which does depend on fold change.

Reading the data

Functional annotation is in 2019-07-26. I will also upload two lists of genes, with either proportion of variance explained by hatching or p-value of differential expression test.

tagVariance <- read.table(paste0(TAGDIR, VAR, '_variance.txt'))
tagPValue   <- read.table(paste0(TAGDIR, VAR, '_pvalue.txt'))
annotation  <- read.table(ANNOTATION[[TAG]], col.names = c('tagname', 'goterms'))

To initialize the topGOdata object, I will need the gene list as a named numeric vector, where the names are the genes identifiers and the numeric values, either the portion of variance explained by hatching or the p-values of the differential expression test. The structure() function adds attributes to an object.

Variance <- structure(tagVariance[,1], names = row.names(tagVariance))
PValues  <- structure(tagPValue[,1],   names = row.names(tagPValue))
rm(tagVariance, tagPValue)

There are 18598 genes scored with a variance portion and a differential expression p-value. It should actually be the exact same genes. The annotation data frame has more than one GO term for every tag, separated by |. I need a named list.

head(annotation)

##       tagname                                                           goterms
## 1 XLOC_000002                                  GO:0008417|GO:0016020|GO:0006486
## 2 XLOC_000009                                  GO:0043130|GO:0005515|GO:0043161
## 3 XLOC_000010                       GO:0005840|GO:0015935|GO:0003735|GO:0006412
## 4 XLOC_000015 GO:0006355|GO:0003700|GO:0006357|GO:0043565|GO:0005634|GO:0032502
## 5 XLOC_000021                       GO:0016567|GO:0006397|GO:0061630|GO:0008270
## 6 XLOC_000036                                  GO:0005272|GO:0006814|GO:0016020

allgenes2GO <- strsplit(as.character(annotation$goterms), "|", fixed = TRUE)
names(allgenes2GO) <- annotation$tagname
rm(annotation)

There are 9691 genes with GO annotations. But the differential expression analysis includes many more genes. In order to include the not-annotated genes in the enrichment analysis, to see if annotated or not annotated genes are more or less often differentially expressed, I should attribute a GO term to them. According to [http://geneontology.org/docs/faq/] nowadays we express lack of annotation by annotating to the root nodes, i.e. GO:0008150 biological_process, GO:0003674 molecular_function, and GO:0005575 cellular_component.

for (tag in unique(c(names(PValues), names(Variance)))) {
   if (! tag %in% names(allgenes2GO)) {
      allgenes2GO <- append(allgenes2GO,
         structure(list(c("GO:0008150", "GO:0003674", "GO:0005575")), names = tag))
   }
}

Using differential expression p-values

Building the topGO object

Creation of a topGO dataset is documented in section 4 of topGO’s the user manual: https://bioconductor.org/packages/release/bioc/vignettes/topGO/inst/doc/topGO.pdf. I need to use the new command, and fill up the slots. The annot object must be a function that compiles “a list of GO terms such that each element in the list is a character vector containing all the gene identifiers that are mapped to the respective GO term.” There are several options, that you can check using help(annFUN.gene2GO), for example. The annFUN.gene2GO requires a gene2GO argument, which is the list of gene-to-GO terms I made before. The geneSelectionFun object is a function that selects the interesting (most significant) genes. It is required to perform Fisher’s exact test. The nodeSize is used to prune the GO hierarchy from the terms which have less than n annotated genes.

I generate three datasets, to analyse each of the three ontologies.

selection <- function(allScores) {return(allScores < 0.05)}
GOdata.BP <- new('topGOdata',
   description = 'Differential expression among Brachionus plicatilis populations.',
   ontology = 'BP', 
   allGenes = PValues,
   annot = annFUN.gene2GO,
   gene2GO = allgenes2GO,
   geneSelectionFun = selection,
   nodeSize = 5)

GOdata.MF <- new('topGOdata',
   description = 'Differential expression among Brachionus plicatilis populations.',
   ontology = 'MF',
   allGenes = PValues,
   annot = annFUN.gene2GO,
   gene2GO = allgenes2GO,
   geneSelectionFun = selection,
   nodeSize = 5)

GOdata.CC <- new('topGOdata',
   description = 'Differential expression among Brachionus plicatilis populations.',
   ontology = 'CC',
   allGenes = PValues,
   annot = annFUN.gene2GO,
   gene2GO = allgenes2GO,
   geneSelectionFun = selection,
   nodeSize = 5)

DataSummary <- data.frame(ontology = c('BP', 'MF', 'CC'),
   Num_Genes = sapply(list(GOdata.BP, GOdata.MF, GOdata.CC), numGenes),
   Num_GO_terms = sapply(list(GOdata.BP, GOdata.MF, GOdata.CC), function(x) length(usedGO(x))))
kable(DataSummary, caption='Number of feasible genes or transcripts and number of GO terms used in each data set.')
rm(DataSummary)

Number of feasible genes or transcripts and number of GO terms used in each data set.

ontology	Num_Genes	Num_GO_terms
BP	15162	1154
MF	17429	576
CC	12940	291

Running the tests

There are more than one way to test for enrichment. Something that took me a while to understand is that not only there are different test statistics (Fisher’s exact test, Kolmogorov-Smirnov, and others) but also different algorithms: classic, elim, weight… The algorithms are ways to deal with the dependence structure among GO terms due to topology. Some algorithms are compatible with all statistics implemented in topGO. But the weight and the parentchild algorithms are only applicable to Fisher’s exact test. I am not interested in the classic algorithm, which treats GO nodes as independent, and therefore produces an excess of significant results. I will not use the Fisher’s exact test, because it dependes on an arbitrary threshold of significance on non-adjusted p-values.

BP.elim     <- runTest(GOdata.BP, algorithm = "elim",     statistic = "ks")
BP.weight01 <- runTest(GOdata.BP, algorithm = "weight01", statistic = "ks")
BP.lea      <- runTest(GOdata.BP, algorithm = "lea",      statistic = "ks")
MF.elim     <- runTest(GOdata.MF, algorithm = "elim",     statistic = "ks")
MF.weight01 <- runTest(GOdata.MF, algorithm = "weight01", statistic = "ks")
MF.lea      <- runTest(GOdata.MF, algorithm = "lea",      statistic = "ks")
CC.elim     <- runTest(GOdata.CC, algorithm = "elim",     statistic = "ks")
CC.weight01 <- runTest(GOdata.CC, algorithm = "weight01", statistic = "ks")
CC.lea      <- runTest(GOdata.CC, algorithm = "lea",      statistic = "ks")

ResultsSummary <- data.frame(ontology = rep(c("BP", "MF", "CC"), each = 3),
   algorithm = rep(c("elim", "weight01", "lea"), 3),
   TermsTested = sapply(list(BP.elim, BP.weight01, BP.lea, MF.elim, MF.weight01, MF.lea, CC.elim, CC.weight01, CC.lea), function(X) length(score(X))),
   Significant = sapply(list(BP.elim, BP.weight01, BP.lea, MF.elim, MF.weight01, MF.lea, CC.elim, CC.weight01, CC.lea), function(X) sum(score(X) < 0.01)))

kable(ResultsSummary, caption="Number of non-trivial terms tested and those with a score (not corrected p-value) lower than 0.01.")

Number of non-trivial terms tested and those with a score (not corrected p-value) lower than 0.01.

ontology	algorithm	TermsTested	Significant
BP	elim	1154	21
BP	weight01	1154	12
BP	lea	1154	51
MF	elim	576	13
MF	weight01	576	14
MF	lea	576	22
CC	elim	291	6
CC	weight01	291	4
CC	lea	291	9

rm(ResultsSummary)

Results

The topGO package does not pay much attention to what terms are significant because they are overrepresented and which ones are underrepresented among the most differentially expressed genes. I think it’s worth separating them, to facilitate the biological interpretation. Note that not all terms listed in the tables below are significant. The scores for the three methods (elim, weight01 and lea) are non-corrected p-values.

Biological process

orderedTerms <- names(sort(score(BP.weight01)))
significant.weight01 <- score(BP.weight01)[orderedTerms] <= 0.01
significant.lea      <- score(BP.lea)[orderedTerms] <= 0.01
significant.elim     <- score(BP.elim)[orderedTerms] <= 0.01
sigTerms <- orderedTerms[significant.weight01 & significant.lea & significant.elim]
# sigTerms gets updated, and is already used in the code, but I need a permanent copy for later.
BP.pvalue.sigTerms <- sigTerms

BP.all <- GenTable(GOdata.BP, elim=BP.elim, weight01=BP.weight01, lea=BP.lea,
                   orderBy="weight01", ranksOf="elim", topNodes=sum(significant.elim))

kable(
   BP.all[BP.all$Significant > BP.all$Expected,],
   caption = "Most over-represented terms of the Biological Process ontology.")

Most over-represented terms of the Biological Process ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
2	GO:0006486	protein glycosylation	75	5	2.96	4	0.0014	0.0011	0.00135
4	GO:1901264	carbohydrate derivative transport	11	2	0.43	199	0.1221	0.0029	0.12212
5	GO:0015931	nucleobase-containing compound transport	29	2	1.14	504	0.4185	0.0029	0.41849
7	GO:0034314	Arp2/3 complex-mediated actin nucleation	12	2	0.47	7	0.0036	0.0036	0.00357
9	GO:0072330	monocarboxylic acid biosynthetic process	24	2	0.95	600	0.5131	0.0045	0.51711
11	GO:0009968	negative regulation of signal transducti…	9	1	0.35	8	0.0036	0.0065	0.00362
13	GO:0003341	cilium movement	10	1	0.39	22	0.0112	0.0112	0.01125
14	GO:0001522	pseudouridine synthesis	13	1	0.51	23	0.0113	0.0113	0.01132
15	GO:0035435	phosphate ion transmembrane transport	8	1	0.32	25	0.0114	0.0114	0.01138
16	GO:0044341	sodium-dependent phosphate transport	8	1	0.32	26	0.0114	0.0114	0.01138

kable(
   BP.all[BP.all$Significant < BP.all$Expected,],
   caption = "Most under-represented terms of the Biological Process ontology.")

Most under-represented terms of the Biological Process ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
1	GO:0060271	cilium assembly	46	1	1.81	1	5.9e-07	6.4e-06	5.9e-07
3	GO:0046907	intracellular transport	202	6	7.97	448	0.3620	0.0015	0.36202
6	GO:0007264	small GTPase mediated signal transductio…	81	2	3.19	10	0.0039	0.0033	0.00393
8	GO:0006418	tRNA aminoacylation for protein translat…	40	0	1.58	11	0.0042	0.0042	0.00421
10	GO:0043604	amide biosynthetic process	215	5	8.48	713	0.6214	0.0046	0.50026
12	GO:0016579	protein deubiquitination	40	1	1.58	16	0.0067	0.0067	0.00674
17	GO:0006511	ubiquitin-dependent protein catabolic pr…	102	2	4.02	677	0.5920	0.0121	0.59197
18	GO:0006012	galactose metabolic process	6	0	0.24	33	0.0146	0.0146	0.01462
19	GO:0035556	intracellular signal transduction	173	6	6.82	18	0.0081	0.0160	0.00024
20	GO:0098813	nuclear chromosome segregation	27	1	1.06	465	0.3725	0.0174	0.37246
21	GO:1901135	carbohydrate derivative metabolic proces…	300	11	11.83	384	0.2854	0.0195	0.45408

vennDiagram(vennCounts(cbind(weight01=significant.weight01,
                             lea=significant.lea,
                             elim=significant.elim)))

kable(data.frame(Term = Term(GOTERM[sigTerms]),
                 Definition = Definition(GOTERM[sigTerms]),
                 PValue=score(BP.weight01)[sigTerms]),
      caption = paste('Biological process terms significantly associated with',
                      VAR, 'according to all 3 algorithms', sep=' '))

Biological process terms significantly associated with hatching according to all 3 algorithms

	Term	Definition	PValue
GO:0060271	cilium assembly	The assembly of a cilium, a specialized eukaryotic organelle that consists of a filiform extrusion of the cell surface. Each cilium is bounded by an extrusion of the cytoplasmic membrane, and contains a regular longitudinal array of microtubules, anchored basally in a centriole.	0.0000064
GO:0006486	protein glycosylation	A protein modification process that results in the addition of a carbohydrate or carbohydrate derivative unit to a protein amino acid, e.g. the addition of glycan chains to proteins.	0.0010653
GO:0007264	small GTPase mediated signal transduction	Any series of molecular signals in which a small monomeric GTPase relays one or more of the signals.	0.0033357
GO:0034314	Arp2/3 complex-mediated actin nucleation	The actin nucleation process in which actin monomers combine to form a new branch on the side of an existing actin filament; mediated by the Arp2/3 protein complex and its interaction with other proteins.	0.0035728
GO:0006418	tRNA aminoacylation for protein translation	The synthesis of aminoacyl tRNA by the formation of an ester bond between the 3’-hydroxyl group of the most 3’ adenosine of the tRNA and the alpha carboxylic acid group of an amino acid, to be used in ribosome-mediated polypeptide synthesis.	0.0042091
GO:0009968	negative regulation of signal transduction	Any process that stops, prevents, or reduces the frequency, rate or extent of signal transduction.	0.0065332
GO:0016579	protein deubiquitination	The removal of one or more ubiquitin groups from a protein.	0.0067352

I think the GO graph is useful to see the relationship among the significant terms. But too large graphs are impossible to read. I don’t know how to split the graph in meaningful subgraphs.

showSigOfNodes(GOdata.BP, score(BP.weight01),
               firstSigNodes = sum(significant.elim),
               wantedNodes = sigTerms)

## $dag
## A graphNEL graph with directed edges
## Number of Nodes = 179 
## Number of Edges = 335 
## 
## $complete.dag
## [1] "A graph with 179 nodes."

This is just a example of the most significant GO term:

showGroupDensity(GOdata.BP, names(score(BP.weight01))[which.min(score(BP.weight01))])

Molecular function

orderedTerms <- names(sort(score(MF.weight01)))
significant.weight01 <- score(MF.weight01)[orderedTerms] <= 0.01
significant.lea      <- score(MF.lea)[orderedTerms] <= 0.01
significant.elim     <- score(MF.elim)[orderedTerms] <= 0.01
sigTerms <- orderedTerms[significant.weight01 & significant.lea & significant.elim]
# sigTerms gets updated, and is already used in the code, but I need a permanent copy for later.
MF.pvalue.sigTerms <- sigTerms

MF.all <- GenTable(GOdata.MF, elim=MF.elim, weight01=MF.weight01, lea=MF.lea,
                   orderBy="weight01", ranksOf="elim", topNodes=sum(significant.elim))

kable(
   MF.all[MF.all$Significant > MF.all$Expected,],
   caption = "Most over-represented terms of the Molecular Function ontology.")

Most over-represented terms of the Molecular Function ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
2	GO:0008417	fucosyltransferase activity	33	4	1.27	3	0.00066	0.00066	0.00066
6	GO:0016757	transferase activity, transferring glyco…	194	10	7.46	7	0.00287	0.00285	1.7e-06
7	GO:1901505	carbohydrate derivative transmembrane tr…	22	2	0.85	306	0.48252	0.00289	0.48252
10	GO:0004842	ubiquitin-protein transferase activity	76	3	2.92	152	0.18382	0.00661	0.18382
11	GO:0005085	guanyl-nucleotide exchange factor activi…	58	3	2.23	60	0.04246	0.00691	0.04246
12	GO:0008061	chitin binding	77	5	2.96	11	0.00721	0.00721	0.00721

kable(
   MF.all[MF.all$Significant < MF.all$Expected,],
   caption = "Most under-represented terms of the Molecular Function ontology.")

Most under-represented terms of the Molecular Function ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
1	GO:0005515	protein binding	2101	67	80.77	1	3.4e-08	1.3e-10	1.0e-09
3	GO:0005509	calcium ion binding	361	11	13.88	4	0.00123	0.00123	0.00123
4	GO:0036459	thiol-dependent ubiquitinyl hydrolase ac…	43	1	1.65	28	0.01699	0.00229	0.01699
5	GO:0004812	aminoacyl-tRNA ligase activity	42	0	1.61	6	0.00231	0.00231	0.00231
8	GO:0008536	Ran GTPase binding	14	0	0.54	8	0.00322	0.00322	0.00322
9	GO:0004707	MAP kinase activity	6	0	0.23	9	0.00591	0.00591	0.00591
13	GO:0005524	ATP binding	786	19	30.22	12	0.00870	0.00870	0.00870

vennDiagram(vennCounts(cbind(weight01=significant.weight01,
                             lea=significant.lea,
                             elim=significant.elim)))

kable(data.frame(Term=Term(GOTERM[sigTerms]),
                 Definition=Definition(GOTERM[sigTerms]),
                 PValue=score(MF.weight01)[sigTerms]),
      caption = paste('Molecular function terms significantly associated with', VAR,
                      'according to all 3 algorithms', sep=' '))

Molecular function terms significantly associated with hatching according to all 3 algorithms

	Term	Definition	PValue
GO:0005515	protein binding	Interacting selectively and non-covalently with any protein or protein complex (a complex of two or more proteins that may include other nonprotein molecules).	0.0000000
GO:0008417	fucosyltransferase activity	Catalysis of the transfer of a fucosyl group to an acceptor molecule, typically another carbohydrate or a lipid.	0.0006623
GO:0005509	calcium ion binding	Interacting selectively and non-covalently with calcium ions (Ca2+).	0.0012279
GO:0004812	aminoacyl-tRNA ligase activity	Catalysis of the formation of aminoacyl-tRNA from ATP, amino acid, and tRNA with the release of diphosphate and AMP.	0.0023073
GO:0016757	transferase activity, transferring glycosyl groups	Catalysis of the transfer of a glycosyl group from one compound (donor) to another (acceptor).	0.0028549
GO:0008536	Ran GTPase binding	Interacting selectively and non-covalently with Ran, a conserved Ras-like GTP-binding protein, implicated in nucleocytoplasmic transport, cell cycle progression, spindle assembly, nuclear organization and nuclear envelope (NE) assembly.	0.0032245
GO:0004707	MAP kinase activity	Catalysis of the reaction: protein + ATP = protein phosphate + ADP. This reaction is the phosphorylation of proteins. Mitogen-activated protein kinase; a family of protein kinases that perform a crucial step in relaying signals from the plasma membrane to the nucleus. They are activated by a wide range of proliferation- or differentiation-inducing signals; activation is strong with agonists such as polypeptide growth factors and tumor-promoting phorbol esters, but weak (in most cell backgrounds) by stress stimuli.	0.0059098
GO:0008061	chitin binding	Interacting selectively and non-covalently with chitin, a linear polysaccharide consisting of beta-(1->4)-linked N-acetyl-D-glucosamine residues.	0.0072072
GO:0005524	ATP binding	Interacting selectively and non-covalently with ATP, adenosine 5’-triphosphate, a universally important coenzyme and enzyme regulator.	0.0086997

showSigOfNodes(GOdata.MF, score(MF.weight01),
               firstSigNodes = sum(significant.elim),
               wantedNodes = sigTerms)

## $dag
## A graphNEL graph with directed edges
## Number of Nodes = 59 
## Number of Edges = 75 
## 
## $complete.dag
## [1] "A graph with 59 nodes."

showGroupDensity(GOdata.MF, names(score(MF.weight01))[which.min(score(MF.weight01))])

Cellular component

orderedTerms <- names(sort(score(CC.weight01)))
significant.weight01 <- score(CC.weight01)[orderedTerms] <= 0.01
significant.lea      <- score(CC.lea)[orderedTerms] <= 0.01
significant.elim     <- score(CC.elim)[orderedTerms] <= 0.01
sigTerms <- orderedTerms[significant.weight01 & significant.lea & significant.elim]
# sigTerms gets updated, and is already used in the code, but I need a permanent copy for later.
CC.pvalue.sigTerms <- sigTerms

CC.all <- GenTable(GOdata.CC, elim=CC.elim, weight01=CC.weight01, lea=CC.lea,
                   orderBy="weight01", ranksOf="elim", topNodes=sum(significant.elim))
kable(
   CC.all[CC.all$Significant > CC.all$Expected,],
   caption = "Most over-represented terms of the Cellular Component ontology.")

Most over-represented terms of the Cellular Component ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
3	GO:0005815	microtubule organizing center	37	2	1.46	9	0.01404	0.0042	0.01404
4	GO:0005885	Arp2/3 protein complex	8	2	0.32	2	0.00811	0.0081	0.00811

kable(
   CC.all[CC.all$Significant < CC.all$Expected,],
   caption = "Most under-represented terms of the Cellular Component ontology.")

Most under-represented terms of the Cellular Component ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
1	GO:0030286	dynein complex	26	0	1.02	1	0.00023	0.0021	0.00023
2	GO:0032991	protein-containing complex	886	20	34.92	29	0.03995	0.0039	0.03286
5	GO:0005680	anaphase-promoting complex	7	0	0.28	7	0.01138	0.0114	0.01138
6	GO:0044428	nuclear part	236	4	9.30	38	0.04776	0.0138	0.07751

vennDiagram(vennCounts(cbind(weight01=significant.weight01,
                             lea=significant.lea,
                             elim=significant.elim)))

kable(data.frame(Term=Term(GOTERM[sigTerms]),
                 Definition=Definition(GOTERM[sigTerms]),
                 PValue=score(CC.weight01)[sigTerms]),
      caption = paste('Cellular component terms significantly associated with', VAR,
                      'according to all 3 algorithms', sep=' '))

Cellular component terms significantly associated with hatching according to all 3 algorithms

	Term	Definition	PValue
GO:0030286	dynein complex	Any of several large complexes that contain two or three dynein heavy chains and several light chains, and have microtubule motor activity.	0.0020997
GO:0005885	Arp2/3 protein complex	A stable protein complex that contains two actin-related proteins, Arp2 and Arp3, and five novel proteins (ARPC1-5), and functions in the nucleation of branched actin filaments.	0.0081061

showSigOfNodes(GOdata.CC, score(CC.weight01),
               firstSigNodes = sum(significant.elim),
               wantedNodes = sigTerms)

## $dag
## A graphNEL graph with directed edges
## Number of Nodes = 30 
## Number of Edges = 48 
## 
## $complete.dag
## [1] "A graph with 30 nodes."

showGroupDensity(GOdata.CC, names(score(CC.weight01))[which.min(score(CC.weight01))])

Using the portion of variance explained by hatching

Building the topGO object

I need to generate the topGO objects again, using the alternative gene ordering, based on the proportion of expression-level variance explained by hatching. I miss a way to inform the topGOdata object that the score in this case is reversed, with respect to p-values: the higher it is, the more differentially expressed the gene is. To make sure that GO terms are tested in the same way than when using p-values, I will just reverse the proportion of variance explained by hatching to its complement. Taking this into account, the subset of interesting genes (selection() function) must be defined as the lowest 10% scores, which are the 10% genes with largest portion of variance explained by hatching.

selection <- function(allScores) {return(allScores <= quantile(allScores, probs = 0.10))}
GOdataVar.BP <- new('topGOdata',
   description = 'Differential expression among Brachionus plicatilis populations.',
   ontology = 'BP', 
   allGenes = 1.0 - Variance,
   annot = annFUN.gene2GO,
   gene2GO = allgenes2GO,
   geneSelectionFun = selection,
   nodeSize = 5)

GOdataVar.MF <- new('topGOdata',
   description = 'Differential expression among Brachionus plicatilis populations.',
   ontology = 'MF',
   allGenes = 1.0 - Variance,
   annot = annFUN.gene2GO,
   gene2GO = allgenes2GO,
   geneSelectionFun = selection,
   nodeSize = 5)

GOdataVar.CC <- new('topGOdata',
   description = 'Differential expression among Brachionus plicatilis populations.',
   ontology = 'CC',
   allGenes = 1.0 - Variance,
   annot = annFUN.gene2GO,
   gene2GO = allgenes2GO,
   geneSelectionFun = selection,
   nodeSize = 5)

library(knitr)
DataSummary <- data.frame(ontology = c('BP', 'MF', 'CC'),
   Num_Genes = sapply(list(GOdataVar.BP, GOdataVar.MF, GOdataVar.CC), numGenes),
   Num_GO_terms = sapply(list(GOdataVar.BP, GOdataVar.MF, GOdataVar.CC), function(x) length(usedGO(x))))
kable(DataSummary, caption='Number of feasible genes or transcripts and number of GO terms used in each data set.')
rm(DataSummary)

Number of feasible genes or transcripts and number of GO terms used in each data set.

ontology	Num_Genes	Num_GO_terms
BP	15162	1154
MF	17429	576
CC	12940	291

Running the tests

BPvar.elim     <- runTest(GOdataVar.BP, algorithm = "elim",     statistic = "ks")
BPvar.weight01 <- runTest(GOdataVar.BP, algorithm = "weight01", statistic = "ks")
BPvar.lea      <- runTest(GOdataVar.BP, algorithm = "lea",      statistic = "ks")
MFvar.elim     <- runTest(GOdataVar.MF, algorithm = "elim",     statistic = "ks")
MFvar.weight01 <- runTest(GOdataVar.MF, algorithm = "weight01", statistic = "ks")
MFvar.lea      <- runTest(GOdataVar.MF, algorithm = "lea",      statistic = "ks")
CCvar.elim     <- runTest(GOdataVar.CC, algorithm = "elim",     statistic = "ks")
CCvar.weight01 <- runTest(GOdataVar.CC, algorithm = "weight01", statistic = "ks")
CCvar.lea      <- runTest(GOdataVar.CC, algorithm = "lea",      statistic = "ks")

ResultsSummary <- data.frame(ontology = rep(c("BP", "MF", "CC"), each = 3),
   algorithm = rep(c("elim", "weight01", "lea"), 3),
   TermsTested = sapply(list(BPvar.elim, BPvar.weight01, BPvar.lea, MFvar.elim, MFvar.weight01, MFvar.lea, CCvar.elim, CCvar.weight01, CCvar.lea), function(X) length(score(X))),
   Significant = sapply(list(BPvar.elim, BPvar.weight01, BPvar.lea, MFvar.elim, MFvar.weight01, MFvar.lea, CCvar.elim, CCvar.weight01, CCvar.lea), function(X) sum(score(X) < 0.01)))

kable(ResultsSummary, caption="Number of non-trivial terms tested and those with a score (not corrected p-value) lower than 0.01.")

Number of non-trivial terms tested and those with a score (not corrected p-value) lower than 0.01.

ontology	algorithm	TermsTested	Significant
BP	elim	1154	6
BP	weight01	1154	5
BP	lea	1154	9
MF	elim	576	5
MF	weight01	576	4
MF	lea	576	7
CC	elim	291	1
CC	weight01	291	0
CC	lea	291	1

rm(ResultsSummary)

Results

Biological process

orderedTerms <- names(sort(score(BPvar.weight01)))
significant.weight01 <- score(BPvar.weight01)[orderedTerms] <= 0.01
significant.lea      <- score(BPvar.lea)[orderedTerms] <= 0.01
significant.elim     <- score(BPvar.elim)[orderedTerms] <= 0.01
sigTerms <- orderedTerms[significant.weight01 & significant.lea & significant.elim]
# sigTerms gets updated, and is already used in the code, but I need a permanent copy for later.
BP.variance.sigTerms <- sigTerms

BPvar.all <- GenTable(GOdataVar.BP, elim=BPvar.elim, weight01=BPvar.weight01, lea=BPvar.lea,
                      orderBy="weight01", ranksOf="elim", topNodes=sum(significant.elim))

kable(
   BPvar.all[BPvar.all$Significant > BPvar.all$Expected,],
   caption = "Most over-represented terms of the Biological Process ontology.")

Most over-represented terms of the Biological Process ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
1	GO:0006887	exocytosis	26	4	2.72	26	0.0210	0.0037	0.0210
6	GO:0000902	cell morphogenesis	10	5	1.04	7	0.0101	0.0101	0.0101

kable(
   BPvar.all[BPvar.all$Significant < BPvar.all$Expected,],
   caption = "Most under-represented terms of the Biological Process ontology.")

Most under-represented terms of the Biological Process ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
2	GO:0003341	cilium movement	10	1	1.04	3	0.0068	0.0068	0.0068
3	GO:1901264	carbohydrate derivative transport	11	1	1.15	381	0.3229	0.0085	0.3229
4	GO:0015931	nucleobase-containing compound transport	29	1	3.03	643	0.6196	0.0085	0.6196
5	GO:0046907	intracellular transport	202	19	21.10	458	0.4219	0.0100	0.4356

vennDiagram(vennCounts(cbind(weight01=significant.weight01,
                             lea=significant.lea,
                             elim=significant.elim)))

kable(data.frame(Term=Term(GOTERM[sigTerms]),
                 Definition=Definition(GOTERM[sigTerms]),
                 PValue=score(BPvar.weight01)[sigTerms]),
      caption = paste('Biological process terms significantly associated with', VAR,
                      'according to all 3 algorithms', sep=' '))

Biological process terms significantly associated with hatching according to all 3 algorithms

	Term	Definition	PValue
GO:0003341	cilium movement	The directed, self-propelled movement of a cilium.	0.0068139

showSigOfNodes(GOdataVar.BP, score(BPvar.weight01),
               firstSigNodes = sum(significant.elim),
               wantedNodes = sigTerms)

## $dag
## A graphNEL graph with directed edges
## Number of Nodes = 28 
## Number of Edges = 39 
## 
## $complete.dag
## [1] "A graph with 28 nodes."

Below I plot variance portion, but for the termo found most significant when using p-values, for comparison.

showGroupDensity(GOdataVar.BP, names(score(BP.weight01))[which.min(score(BP.weight01))])

Molecular function

orderedTerms <- names(sort(score(MFvar.weight01)))
significant.weight01 <- score(MFvar.weight01)[orderedTerms] <= 0.01
significant.lea      <- score(MFvar.lea)[orderedTerms] <= 0.01
significant.elim     <- score(MFvar.elim)[orderedTerms] <= 0.01
sigTerms <- orderedTerms[significant.weight01 & significant.lea & significant.elim]
# sigTerms gets updated, and is already used in the code, but I need a permanent copy for later.
MF.variance.sigTerms <- sigTerms

MFvar.all <- GenTable(GOdataVar.MF, elim=MFvar.elim, weight01=MFvar.weight01, lea=MFvar.lea,
                      orderBy="weight01", ranksOf="elim", topNodes=sum(significant.elim))
kable(
   MFvar.all[MFvar.all$Significant > MFvar.all$Expected,],
   caption = "Most over-represented terms of the Molecular Function ontology.")

Most over-represented terms of the Molecular Function ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
2	GO:0008417	fucosyltransferase activity	33	8	3.33	3	0.00347	0.00347	0.00347

kable(
   MFvar.all[MFvar.all$Significant < MFvar.all$Expected,],
   caption = "Most under-represented terms of the Molecular Function ontology.")

Most under-represented terms of the Molecular Function ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
1	GO:0005515	protein binding	2101	185	212.04	1	0.00098	0.00072	0.00028
3	GO:0140101	catalytic activity, acting on a tRNA	69	4	6.96	425	0.85535	0.00684	0.85535
4	GO:1901505	carbohydrate derivative transmembrane tr…	22	1	2.22	239	0.50759	0.00790	0.50759
5	GO:0042578	phosphoric ester hydrolase activity	140	9	14.13	179	0.33849	0.01104	0.61057

vennDiagram(vennCounts(cbind(weight01=significant.weight01,
                             lea=significant.lea,
                             elim=significant.elim)))

kable(data.frame(Term=Term(GOTERM[sigTerms]),
                 Definition=Definition(GOTERM[sigTerms]),
                 PValue=score(MFvar.weight01)[sigTerms]),
      caption = paste('Molecular functions terms significantly associated with', VAR,
                      'according to all 3 algorithms', sep=' '))

Molecular functions terms significantly associated with hatching according to all 3 algorithms

	Term	Definition	PValue
GO:0005515	protein binding	Interacting selectively and non-covalently with any protein or protein complex (a complex of two or more proteins that may include other nonprotein molecules).	0.0007229
GO:0008417	fucosyltransferase activity	Catalysis of the transfer of a fucosyl group to an acceptor molecule, typically another carbohydrate or a lipid.	0.0034656

showSigOfNodes(GOdataVar.MF, score(MFvar.weight01),
               firstSigNodes = sum(significant.elim),
               wantedNodes = sigTerms)

## $dag
## A graphNEL graph with directed edges
## Number of Nodes = 16 
## Number of Edges = 15 
## 
## $complete.dag
## [1] "A graph with 16 nodes."

I plot variance portion, but for the term found most significant when using p-values, for comparison.

showGroupDensity(GOdataVar.MF, names(score(MF.weight01))[which.min(score(MF.weight01))])

Cellular component

orderedTerms <- names(sort(score(CCvar.weight01)))
significant.weight01 <- score(CCvar.weight01)[orderedTerms] <= 0.01
significant.lea      <- score(CCvar.lea)[orderedTerms] <= 0.01
significant.elim     <- score(CCvar.elim)[orderedTerms] <= 0.01
sigTerms <- orderedTerms[significant.weight01 & significant.lea & significant.elim]
if (length(sigTerms) == 0) {
   sigTerms <- orderedTerms[significant.lea & significant.elim]
}
# sigTerms gets updated, and is already used in the code, but I need a permanent copy for later.
CC.variance.sigTerms <- sigTerms

CCvar.all <- GenTable(GOdataVar.CC, elim=CCvar.elim, weight01=CCvar.weight01, lea=CCvar.lea,
                      orderBy="weight01", ranksOf="elim", topNodes=max(sum(significant.elim), 10))

kable(
   CCvar.all[CCvar.all$Significant > CCvar.all$Expected,],
   caption = "Most over-represented terms of the Cellular Component ontology.")

Most over-represented terms of the Cellular Component ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
3	GO:0044440	endosomal part	12	2	1.27	34	0.062	0.020	0.062
4	GO:0005680	anaphase-promoting complex	7	1	0.74	13	0.031	0.031	0.031
5	GO:0005890	sodium:potassium-exchanging ATPase compl…	5	1	0.53	21	0.044	0.044	0.044

kable(
   CCvar.all[CCvar.all$Significant < CCvar.all$Expected,],
   caption = "Most under-represented terms of the Cellular Component ontology.")

Most under-represented terms of the Cellular Component ontology.

	GO.ID	Term	Annotated	Significant	Expected	Rank in elim	elim	weight01	lea
1	GO:0000123	histone acetyltransferase complex	22	2	2.33	30	0.053	0.011	0.053
2	GO:0032991	protein-containing complex	886	65	93.74	201	0.786	0.017	0.966
6	GO:0032580	Golgi cisterna membrane	8	0	0.85	24	0.046	0.046	0.046
7	GO:0044428	nuclear part	236	20	24.97	66	0.184	0.064	0.957
8	GO:0045211	postsynaptic membrane	16	0	1.69	39	0.067	0.067	0.067
9	GO:0044798	nuclear transcription factor complex	25	0	2.64	52	0.108	0.072	0.108
10	GO:1990234	transferase complex	111	6	11.74	65	0.182	0.074	0.880

vennDiagram(vennCounts(cbind(weight01=significant.weight01,
                             lea=significant.lea,
                             elim=significant.elim)))

kable(data.frame(Term=Term(GOTERM[sigTerms]),
                 Definition=Definition(GOTERM[sigTerms]),
                 PValue=score(CCvar.weight01)[sigTerms]),
      caption = paste('Cellular component terms significantly associated with', VAR,
                      'according to all 3 algorithms', sep=' '))

Cellular component terms significantly associated with hatching according to all 3 algorithms

	Term	Definition	PValue
GO:0005929	cilium	A specialized eukaryotic organelle that consists of a filiform extrusion of the cell surface and of some cytoplasmic parts. Each cilium is largely bounded by an extrusion of the cytoplasmic (plasma) membrane, and contains a regular longitudinal array of microtubules, anchored to a basal body.	0.2040169

showSigOfNodes(GOdataVar.CC, score(CCvar.weight01),
               firstSigNodes = sum(significant.weight01),
               wantedNodes = sigTerms)

## $dag
## A graphNEL graph with directed edges
## Number of Nodes = 28 
## Number of Edges = 44 
## 
## $complete.dag
## [1] "A graph with 28 nodes."

For comparison, I plot the distribution of variance portion for the CC term found most significant when using p-values.

showGroupDensity(GOdataVar.CC, names(score(CC.weight01))[which.min(score(CC.weight01))])

Comparison between the two ordering of genes.

Biological process

allTerms <- usedGO(GOdata.BP)
vennDiagram(vennCounts(cbind(PValue   = allTerms %in% BP.pvalue.sigTerms,
                             Variance = allTerms %in% BP.variance.sigTerms)))

ggplot(data = data.frame(PValue   = rank(score(BP.weight01))[allTerms],
                         Variance = rank(score(BPvar.weight01))[allTerms]),
       mapping = aes(x = PValue, y = Variance)) +
   geom_point() + geom_smooth() + xlab('Using gene p-values') +
   ylab('Using portion of explained variance') +
   ggtitle('Ordering of BP terms by significance')

Molecular function

allTerms <- usedGO(GOdata.MF)
vennDiagram(vennCounts(cbind(PValue   = allTerms %in% MF.pvalue.sigTerms,
                             Variance = allTerms %in% MF.variance.sigTerms)))

ggplot(data = data.frame(PValue   = rank(score(MF.weight01))[allTerms],
                         Variance = rank(score(MFvar.weight01))[allTerms]),
       mapping = aes(x = PValue, y = Variance)) +
   geom_point() + geom_smooth() + xlab('Using gene p-values') +
   ylab('Using portion of explained variance') +
   ggtitle('Ordering of MF terms by significance')

Cellular component

allTerms <- usedGO(GOdata.CC)
vennDiagram(vennCounts(cbind(PValue   = allTerms %in% CC.pvalue.sigTerms,
                             Variance = allTerms %in% CC.variance.sigTerms)))

ggplot(data = data.frame(PValue   = rank(score(CC.weight01))[allTerms],
                         Variance = rank(score(CCvar.weight01))[allTerms]),
       mapping = aes(x = PValue, y = Variance)) +
   geom_point() + geom_smooth() + xlab('Using gene p-values') +
   ylab('Using portion of explained variance') +
   ggtitle('Ordering of CC terms by significance')

Session info

I save the main variables to be able to load them in a new R session later.

save(allgenes2GO,
     GOdata.BP, BP.elim, BP.weight01, BP.lea, BP.pvalue.sigTerms,
     GOdata.MF, MF.elim, MF.weight01, MF.lea, MF.pvalue.sigTerms,
     GOdata.CC, CC.elim, CC.weight01, CC.lea, CC.pvalue.sigTerms,
     GOdataVar.BP, BPvar.elim, BPvar.weight01, BPvar.lea, BP.variance.sigTerms,
     GOdataVar.MF, MFvar.elim, MFvar.weight01, MFvar.lea, MF.variance.sigTerms,
     GOdataVar.CC, CCvar.elim, CCvar.weight01, CCvar.lea, CC.variance.sigTerms,
     file = paste('Enrichment', TAG, VAR, 'RData', sep='.'))
sessionInfo()

## R version 3.6.2 (2019-12-12)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
## 
## locale:
##  [1] LC_CTYPE=ca_ES.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=es_ES.UTF-8        LC_COLLATE=ca_ES.UTF-8    
##  [5] LC_MONETARY=es_ES.UTF-8    LC_MESSAGES=ca_ES.UTF-8   
##  [7] LC_PAPER=es_ES.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=es_ES.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
##  [1] grid      stats4    parallel  stats     graphics  grDevices utils    
##  [8] datasets  methods   base     
## 
## other attached packages:
##  [1] Rgraphviz_2.30.0     ggplot2_3.2.1        limma_3.42.0        
##  [4] knitr_1.27           topGO_2.38.1         SparseM_1.78        
##  [7] GO.db_3.10.0         AnnotationDbi_1.48.0 IRanges_2.20.2      
## [10] S4Vectors_0.24.3     Biobase_2.46.0       graph_1.64.0        
## [13] BiocGenerics_0.32.0 
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_0.2.5   xfun_0.12          purrr_0.3.3        splines_3.6.2     
##  [5] lattice_0.20-38    colorspace_1.4-1   vctrs_0.2.1        htmltools_0.4.0   
##  [9] yaml_2.2.0         mgcv_1.8-31        blob_1.2.1         rlang_0.4.2       
## [13] pillar_1.4.3       glue_1.3.1         withr_2.1.2        DBI_1.1.0         
## [17] bit64_0.9-7        matrixStats_0.55.0 lifecycle_0.1.0    stringr_1.4.0     
## [21] munsell_0.5.0      gtable_0.3.0       memoise_1.1.0      evaluate_0.14     
## [25] labeling_0.3       highr_0.8          Rcpp_1.0.3         backports_1.1.5   
## [29] scales_1.1.0       farver_2.0.3       bit_1.1-15.1       digest_0.6.23     
## [33] stringi_1.4.5      dplyr_0.8.3        tools_3.6.2        magrittr_1.5      
## [37] lazyeval_0.2.2     tibble_2.1.3       RSQLite_2.2.0      crayon_1.3.4      
## [41] pkgconfig_2.0.3    zeallot_0.1.0      Matrix_1.2-18      assertthat_0.2.1  
## [45] rmarkdown_2.1      R6_2.4.1           nlme_3.1-143       compiler_3.6.2